What is a field?

According to me, a field is a collection of points in space such that at each point in space, the value of the property(variable or constant) is a function of the position of that point with respect to a reference. In case of vector fields, besides the value, an arrow is associated to the point which gives the direction.

For example:
An electric field is a collection of points in space such that the electric field intensity at each point in space, is a function of the position of that point with respect to position of the source charge. In addition to the value, an arrow is associated to the point which indicates the direction in which a test charge would experience a force.

Your statements are correct, but wording in them is very redundant. If you already have the concept "function of position", then you can say "a field is a function of position". The function can be scalar or vectorial, giving scalar or vector fields. The most general kind of field is the tensor field (the value of the function is a tensor).

I'd argue that this isn't really correct or, at best, ambiguous. Are you saying the field consists of points in space (in which case you're saying the field is space)? If not, what exactly do you mean by points?

such that at each point in space, the value of the property(variable or constant) is a function of the position of that point with respect to a reference. In case of vector fields, besides the value, an arrow is associated to the point which gives the direction.

It's unnecessary to use the magnitude-and-direction representation of a vector, and I think it doesn't really help because it's hard to generalize to other types of fields. As voko noted, you can simply say there's a vector assigned to each point in space.

For example:
An electric field is a collection of points in space such that the electric field intensity at each point in space, is a function of the position of that point with respect to position of the source charge. In addition to the value, an arrow is associated to the point which indicates the direction in which a test charge would experience a force.

The problem I'd have here is that for each point in space, you're equating the electric field, which is a three-dimensional vector, to a point, which is a zero-dimensional object. I realize that's not what you meant, but you should find a better way to express your ideas. For one, don't use the term point to refer to the field.

rohit..you are on the right track...defining what a field 'is' is tricky.

A field is an extended theoretical concept we use to describe actions, like particle interactions. We can't detect fields. Everytime we observe [detect] a field we observe, that is record, a point particle. Whether field theory is 'real' or not is a philosophical question; the 'point' is [pun intended] they have proven to be an extremely useful description of experimental observations.

You can get a view of fields in physics here:

http://en.wikipedia.org/wiki/Field_(physics [Broken])

A field is a physical quantity that has a value for each point in space and time.[1]

According to me, a field is a collection of points in space such that at each point in space, the value of the property(variable or constant) is a function of the position of that point with respect to a reference. In case of vector fields, besides the value, an arrow is associated to the point which gives the direction.

For example:
An electric field is a collection of points in space such that the electric field intensity at each point in space, is a function of the position of that point with respect to position of the source charge. In addition to the value, an arrow is associated to the point which indicates the direction in which a test charge would experience a force.

I would like to know if my statement is right.

A field is something real like the mass. An electric field has/stores energy. A field does not need anything else to exist. The light you see coming from a star exists even the star does not exist anymore.

what is 'real' is what you measure, what you detect. The closest I've come to observing a field are magnetic lines of force aligning magnetic particles.

An electric field has/stores energy.

While that IS the theory we ascribe to a field, elsewhere we don't use fields, like gravity in relativity. Does a gravitational 'field' exist just because it has energy, can do work? Many would say no, the the Newtonian field approximation is just an abstract model which works in simple cases.

A field does not need anything else to exist.

It needs space and time and probably a source depending what you mean.

The light you see coming from a star exists even the star does not exist anymore.

Due to the finite propagation speed of light, photons arriving at your eye may be billions of years old, so their source may have died out long ago.

A field is real because it carries energy.

We cannot directly observe a field. What is 'real' depends on what you define it to be.

When you detect light, for example, you are detecting 'particles', quanta [local excitations] of the underlying field.

You could also claim with some authority 'a field is 'real' because it supports all our experimental observations. Many would not agree that is a good definition.

That is not true in general. A velocity field needs something that has velocities. A temperature field needs something that has temperature. A deformation field needs something that can deform.

A field is real because it carries energy

What do you mean by "carry"? There are two interpretations: "transport" or "be associated with". An electrostatic field does not transport anything by definition. It is associated with energy, but everything we can detect can be associated with energy in one way or another, so that is not a useful specification.